Difurcating ‘Knowing P’ and ‘Knowing P to be true’

William Lane Craig has argued that the difference between ‘Billy the Hippo is fat’ and ‘the proposition Billy the Hippo is fat is true’ is one of semantic ascent. One semantically ascends when moving from a claim of the first kind to a claim of the second kind, and, conversely, semantically descends when going from a claim of the second kind to a claim of the first kind. He says:

I could say “Hitler was a really bad man.” Or I could ascend semantically and say “It is true that Hitler was a really bad man.” Do you see the difference between the first order and the second level claim? And that second level claim doesn’t need to be made—I can just say “Hitler was a really bad man,” and I can make that affirmation sincerely and so forth without ascending semantically to saying, therefore there is a proposition which has the value true.[1]

I used to think this was right (though I’ve always been a little suspicious of it), but I think I’ve come across a reason to think that it may be wrong. I think that going from ‘Hitler was a really bad man’ to ‘it is true that Hitler was a really bad man’ is not merely a semantic ascent; it also involves the acquisition of new semantic content. Strictly speaking, it expresses a new proposition altogether. I will argue in what follows that one can know that Hitler is a bad man without knowing that the proposition ‘Hitler is a bad man’ is true, and one can also know that the proposition ‘Hitler is a ban man’ is true without knowing that Hitler is a bad man. Perhaps Craig could say that just because two propositions are related in this kind of ‘semantic order,’ knowing one needn’t entail knowing the other. This, in fact, is what he should say; he should deny that the two expressions have all and only the same semantic content. Maybe he does deny this (I don’t know), but I will try to argue that he (and we all) should.

One can know that Hitler is a bad man without knowing that the proposition ‘Hitler is a bad man’ is true because a necessary condition on knowledge is belief, but there is no psychologically necessary connection between knowing that Hitler has the property of being a bad man, and knowing that a proposition (about Hitler’s being a bad man) has the property of being true. After all, when one knows that the proposition “Hitler is a bad man” is true, one doesn’t necessarily believe that the proposition that “the proposition that “Hitler is a bad man” is true” is true. In fact, if that were psychologically necessary then it would follow that by knowing any one proposition one would, of psychological necessity, know infinitely many propositions, and this is absurd. Ergo, one can know that the content expressed by a proposition is true without knowing that the proposition itself has the truth-value ‘true.’

One can also know that a proposition is true without knowing its content. For instance, suppose that there were a being who only ever proclaimed true things (and suppose you were aware of this being having that quality).[2] Suppose further that this being proclaimed to you that proposition P is true. Even if you had only a vague understanding of the content of proposition P (maybe it’s some proposition about quantum mechanics, or actuarial mathematics, or epistemology, or whatever field you may be least familiar with), you could know that it is true. In fact, even if you had no way of making heads or tails of proposition P, you could know that it is true. Therefore, one can know a proposition to be true without believing in its content, and thus without ‘knowing’ its content.

There may be a problem here; we can legitimately wonder whether to know that the proposition P is true requires being properly acquainted with P, and whether to be ‘properly acquainted‘ with P requires an understanding of its content. After all, when I see a man in the distance (who is a stranger to me, but whose name is actually ‘Bill’) break a window, I may know that somebody has broken the window, but I do not know that Bill has broken the window. In the same way I can perhaps know that a proposition is true (namely whatever proposition was uttered by the infallible proclaiming being), without knowing that the proposition (proclaimed by the infallible proclaiming being) is true.

How can one be properly acquainted with a proposition, so as to be able to know whether it is true? If one maintains that one must know what the content of the proposition is in order to be properly acquainted with it, then it will turn out that it may not be possible to know that the proposition “Hitler is a bad man” is true without knowing that Hitler is a bad man. If, on the other hand, it suffices to be able to indicate or ‘pick out’ P from other propositions in some way, such as by saying ‘that proposition’ or ‘the proposition just uttered’ or, perhaps, by repeating/recreating the same combination of sounds/scribbles used to express the proposition in the first place, then obviously one can know a proposition P to be true without knowing its content.

In everyday life we find ourselves doing this all the time. We may hear a professor relate a proposition to us, for instance, and without as of yet having understood it, we know (in the sense of having a true and appropriately justified belief) that it is true. The same may happen in a court of law where an expert witness submits testimony which we can know to be true, even if we haven’t understood that to which the expert is testifying. We also often know propositions to be true, such as “E=MC2,” which few of us have any genuine understanding of. This goes to show that one needn’t be very well acquainted with a proposition in order to know that it is true. Propositional acquaintance comes in degrees, and all one needs in order to know that a proposition is true is enough acquaintance to ‘pick out’ that proposition by some means. If this is right, then to be properly acquainted will require very little, and too little to present any challenge to my argument.

Where does this leave us with respect to Craig’s claim that to move from a claim like that Hitler is a bad man, to a claim like that the proposition Hitler is a bad man is true, is to merely to ascend semantically? It will depend on what Craig means, precisely, by semantic ascent/descent; it should be rejected in light of my observation just in case it does not allow one to maintain i) that the propositional contents in any two propositions related in this ‘order’ of semantic ascent/descent are not identical with each other, and ii) that one can know a truth of either kind without knowing a truth of the other kind. In short, I am calling for a semantic bifurcation of propositions related to each other in a semantic order of ascent/descent.

[1] http://www.reasonablefaith.org/god-abstract-objects-platonism-and-logic#ixzz3q3ZuS4AY

[2] Thanks to Dr. Brian Leftow, who shared this thought in conversation. I had written in an essay that a being was propositionally omniscient if and only if it knew all true propositions and believed no false ones, but later in the same paper I defined propositional omniscience again as follows: a being B is propositionally omniscient if and only if for any proposition P, if P has the property of being true then B knows that it is true, and if P does not have the property of being true then B does not believe it. This clumsy mistake of mine led to more careful reflection on precisely this point; knowing that P is true is not the same as knowing P.

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